Exercise: Logical Deduction

Questions for: Logical Deduction

Statements: Some desks are caps. No cap is red.

Conclusions:

  1. Some caps are desks.
  2. No desk is red.
A:
Only conclusion I follows
B:
Only conclusion II follows
C:
Either I or II follows
D:
Neither I nor II follows
Answer: A
Since one premise is particular and the other premise is negative, the conclusion must be particular negative and should not contain the middle term. So, it follows that 'Some desks are not red'. However, I is the converse of the first premise and thus it holds.
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Statements: Raman is always successful. No fool is always successful.

Conclusions:

  1. Raman is a fool.
  2. Raman is not a fool.
A:
Only conclusion I follows
B:
Only conclusion II follows
C:
Either I or II follows
D:
Neither I nor II follows
Answer: B
Since both the premises are universal and one premise is negative, the conclusion must be universal negative and should not contain the middle term. So, only II follows.
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Statements: All trucks fly. Some scooters fly.

Conclusions:

  1. All trucks are scooters.
  2. Some scooters do not fly.
A:
Only conclusion I follows
B:
Only conclusion II follows
C:
Either I or II follows
D:
Neither I nor II follows
Answer: D
Since the middle term 'fly' is not distributed even once in the premises, no definite conclusion follows.
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Statements: Some books are tables. Some tables are mirrors.

Conclusions:

  1. Some mirrors are books.
  2. No book is mirror.
A:
Only conclusion I follows
B:
Only conclusion II follows
C:
Either I or II follows
D:
Neither I nor II follows
Answer: C
Since both the premises are particular no definite conclusion follows. However, I and II involve only the extreme terms and form a complementary pair. Thus, either I or II follows.
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Statements: All huts are mansions. All mansions are temples.

Conclusions:

  1. Some temples are huts.
  2. Some temples are mansions.
A:
Only conclusion I follows
B:
Only conclusion II follows
C:
Either I or II follows
D:
Neither I nor II follows
Answer: E
As discussed above, it follows that 'All huts are temples'. I is the converse of this conclusion and so it holds. II is the converse of the second premise and so it also holds.
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